Unitarity of generalized fourier-gauss transforms

Un Cig Ji, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


A generalized Fourier-Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.

Original languageEnglish
Pages (from-to)733-751
Number of pages19
JournalStochastic Analysis and Applications
Issue number4
Publication statusPublished - 2006 Aug 1


  • Boson Fock space
  • Fourier-Gauss transform
  • Generalized dilation
  • Generalized Fourier-Gauss transform
  • Kuo's Fourier transform
  • Unitarity
  • White noise theory


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